We need the definition of an indexed grammar introduced in [1]} by following the notation of [2]}, Section 14.3.
An indexed grammar is a 5-tuple \(G = (V, \Sigma , I, P, S)\) , where
\(V, \Sigma , I\)  are finite pairwise disjoint sets: the set of nonterminals, terminals, and indices, respectively, \(S\)  is the start nonterminal, and
\(P\)  is a finite set of productions, each of the form either
\(\mbox{\bf 1)\ } A \rightarrow \nu , \quad \mbox{\bf 2)\ } A \rightarrow Bf, \quad \mbox{or}\quad \mbox{\bf 3)\ } Af \rightarrow \nu ,\) 
